Interest Rate Risk in the Banking Book

Introduction and Context

Interest rate risk in the banking book (IRRBB) is the risk that changes in interest rates adversely affect a bank’s earnings, economic value, capital position, or strategic capacity. It arises because banking-book assets, liabilities and off-balance-sheet items differ in repricing dates, reference rates, maturities, embedded options and behavioural characteristics.

The banking book normally contains loans, deposits, investments intended for relationship or liquidity purposes, wholesale funding and hedging instruments. Unlike trading-book positions, these exposures are generally managed over a longer horizon and are not primarily held for short-term resale. Nevertheless, their values and cash flows respond materially to interest-rate movements.

IRRBB management has two complementary perspectives:

• Earnings perspective: measures the effect of interest-rate changes on future net interest income (NII), usually over a one- to three-year horizon.
• Economic-value perspective: measures the effect of interest-rate changes on the present value of expected cash flows and therefore on the bank’s underlying net worth.

A sound treasury function uses both perspectives. Earnings measures support budgeting, pricing and short-term risk control; economic-value measures reveal longer-term structural vulnerability.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Explain the sources and categories of IRRBB.
2. Construct and interpret repricing-gap, basis-gap and duration measures.
3. Use convexity, earnings-at-risk (EaR) and economic value of equity (EVE) analysis.
4. Evaluate yield-curve, basis and option risks.
5. Model behavioural maturities for non-maturity deposits and prepayments.
6. Assess governance, stress testing, model risk and hedging choices.

1. Sources and Categories of IRRBB

1.1 Repricing risk

Repricing risk results from unequal timing of interest-rate resets. A one-year fixed-rate loan funded by a three-month deposit is exposed when the deposit reprices before the loan. If market rates rise, funding cost may increase while loan income remains fixed.

1.2 Yield-curve risk

Yield-curve risk arises when rates at different maturities change by different amounts. A bank may be hedged against a parallel shift but exposed to a steepening, flattening or inversion. For example, long-term fixed-rate assets and short-term liabilities are particularly vulnerable to a rise in long-term yields or a fall in short-term yields that changes relative margins.

1.3 Basis risk

Basis risk occurs when instruments reprice against different rate indices, such as a loan linked to prime rate and funding linked to a term interbank rate. Even if repricing dates coincide, the spread between the indices can change.

1.4 Option risk

Option risk is created by explicit or implicit choices available to customers or the bank. Examples include fixed-rate loan prepayment, deposit withdrawal, loan-rate caps and floors, callable bonds and early withdrawal provisions. Option exercise is often correlated with interest rates, making cash flows non-linear and uncertain.

1.5 Currency and inflation interactions

Although IRRBB is distinct from foreign-exchange and inflation risk, multi-currency banking books and inflation-linked products can create interactions. Measurement should therefore preserve currency-level detail before aggregation.

2. Repricing-Gap Analysis

For a time bucket i, the rate-sensitive assets (RSAᵢ) and rate-sensitive liabilities (RSLᵢ) are those whose contractual or expected rates reset within that bucket. The simple repricing gap is:

Gᵢ is measured in currency units. A positive gap means more assets than liabilities reprice in the bucket; a negative gap means more liabilities reprice.

The cumulative gap through bucket k is:

Under a simplified parallel rate change Δr, the approximate change in net interest income over the bucket horizon is:

where Δr is the rate change expressed as a decimal and tᵢ is the fraction of a year during which the gap is exposed. The expression assumes instantaneous, full and uniform repricing of all rate-sensitive positions, constant balances, no behavioural changes and no basis or convexity effects. It is therefore a screening measure, not a complete valuation model.

Worked example: simple gap

A bank has the following one-year repricing profile:

All figures are currency millions. In the first bucket, a 1 percentage-point increase in rates lasting three months produces approximately:

∆NII = −60,000,000 × 0.01 × 0.25 = −150,000

The initial negative gap reduces earnings because liabilities reprice upward faster than assets. The calculation does not predict the full-year effect unless the gap and rate change remain applicable for that period.

Limitations of gap analysis

Gap reports can obscure the timing within wide buckets, assume a common rate index and ignore market-value effects. They may also misclassify non-maturity deposits. A deposit with no contractual maturity is not automatically an overnight liability: its behavioural stability must be estimated from evidence and policy constraints.

3. Basis-Gap Analysis

A bank should split repricing exposures by reference rate, not merely by date. Suppose assets indexed to rate A equal Aᵢ and liabilities indexed to rate B equal Bᵢ. The bank’s margin is affected by both the level and the spread between indices:

If the sensitivity to the two indices is represented by notional exposures N_A and N_B, the approximate margin change is:

where Δr_A and Δr_B are decimal rate changes over the relevant period. When N_A = N_B and the indices move identically, basis risk is minimal. When their movements differ, the residual is basis exposure.

A practical basis report groups exposures by index pair, reset tenor and currency. Treasury should monitor historical correlations, stress widening and narrowing of basis spreads, and the liquidity of potential hedging instruments.

4. Duration and Economic-Value Analysis

4.1 Macaulay and modified duration

For a fixed-income instrument with cash flow CFₜ at time t and yield y compounded m times per year, price is:

Macaulay duration is the present-value-weighted average time to receive cash flows:

Modified duration, under a parallel small yield change and fixed cash flows, is:

The first-order price approximation is:

Duration is expressed in years; Δy is a decimal yield change. These formulas assume a conventional fixed-cash-flow instrument, a small parallel shift, a stable yield convention and no embedded option exercise. They are less reliable for large shocks, non-parallel movements and instruments with material optionality.

4.2 Duration of equity

For a simplified balance sheet, let A be the market value of assets, L the market value of liabilities, D_A asset duration and D_L liability duration. Since E = A − L, the approximate change in economic equity for a parallel rate change is:

The duration of equity can be expressed as:

Thus:

This representation is useful only when E is positive and market values and durations are measured consistently. Deposit behaviour, loan prepayments and non-linear instruments require more advanced treatment.

Worked example: EVE sensitivity

Assume market-value assets of 1,000 million with duration 4.2 years and liabilities of 900 million with duration 1.1 years. Equity is 100 million. For a 1 percentage-point parallel increase:

∆E ≈ [−4.2 × 1,000 + 1.1 × 900] × 0.01

∆E ≈ [−4,200 + 990] × 0.01 = −32.1 million

The approximate EVE decline is 32.1 million. The result is highly sensitive to the assumed behavioural duration of liabilities, especially deposits.

5. Convexity and Non-Linear Risk

Duration gives a tangent-line approximation. Convexity improves the approximation when yield changes are larger or when price-yield curvature is material:

where C is convexity, measured in years squared under the relevant convention. For an option-free bond, positive convexity generally reduces the price loss from a rate rise relative to a duration-only estimate. Callable assets and prepayable loans may display negative or state-dependent convexity because borrowers are more likely to exercise when it is advantageous to them.

Convexity must not be used as a substitute for option modelling. A model should re-estimate cash flows when exercise probabilities change.

6. Earnings-at-Risk and Economic Value of Equity

6.1 Earnings-at-risk

EaR estimates the adverse change in NII over a specified horizon under defined rate scenarios. Let NII₀ be baseline NII and NII_s scenario NII. The scenario loss is:

A positive EaR_s indicates a decline in earnings. EaR may be reported as the maximum loss across deterministic scenarios or as a percentile loss under a probabilistic distribution. The choice must be disclosed because deterministic stress loss and statistical VaR are not identical concepts.

EaR requires assumptions about balance-sheet growth, customer pricing, deposit beta, loan prepayment, credit migration, hedge effectiveness and management actions. A static balance sheet isolates rate sensitivity; a dynamic balance sheet may be more realistic but introduces behavioural and strategic assumptions.

6.2 Economic value of equity

EVE is the present value of asset cash flows less the present value of liability and relevant off-balance-sheet cash flows:

For scenario s:

EVE captures long-term value effects even when near-term NII is stable. However, it depends strongly on discount curves, cash-flow assumptions and treatment of commercial margins. EVE and NII can signal different risk directions; neither should be interpreted in isolation.

7. Yield-Curve and Scenario Analysis

A robust scenario set includes:

Scenario design should include both direction and magnitude, preserve economically plausible curve relationships, and consider negative or near-zero rates where relevant. Banks should distinguish between instantaneous shocks and gradual paths because customer repricing, deposit migration and prepayments depend on time.

8. Behavioural Models

8.1 Non-maturity deposits

Current accounts and savings deposits often have no contractual maturity, but balances may be sticky and administered rates may adjust slowly. A behavioural model commonly estimates:

• core and non-core balances;
• expected runoff or decay;
• rate sensitivity, often called deposit beta;
• repricing lag;
• migration between products;
• floors and customer segmentation.

If market rates change by Δr_m and deposit rates change by Δr_d, an empirical deposit beta is:

This is a descriptive ratio, not a universal constant. It may vary by product, customer, rate regime and direction of movement. A deposit model should be calibrated using long historical data, segmented observations and stress testing. Governance should impose a maximum behavioural maturity or average-life assumption, with back-testing against observed runoff and repricing.

8.2 Loan prepayments

For a prepayable fixed-rate loan, the contractual cash-flow schedule is not the expected schedule. A common monthly prepayment measure is the conditional prepayment rate (CPR), derived from the single-month mortality rate (SMM):

Equivalently:

SMM is the proportion of the outstanding balance expected to prepay during a month after scheduled principal effects are treated consistently. The conversion assumes a constant monthly conditional rate and twelve equal periods per year.

Prepayments generally accelerate when market rates fall and refinancing becomes attractive, shortening asset duration. They may slow when rates rise, extending duration precisely when fixed-rate assets lose value. This negative convexity is a central IRRBB concern.

8.3 Model construction and validation

Behavioural models should combine statistical evidence with business judgement. Important practices include segmentation, out-of-sample validation, sensitivity analysis, challenger models, conservative floors and caps, and regular recalibration. Model risk increases after structural breaks, regulatory changes, digital deposit competition or unusual monetary-policy regimes.

9. Integrated Measurement Framework

A professional IRRBB process normally follows these steps:

1. Inventory exposures: capture contractual cash flows, rates, indices, options, currencies and hedges.
2. Clean and classify data: reconcile the risk engine to the general ledger and treasury systems.
3. Map cash flows: assign contractual and behavioural cash flows to repricing and maturity buckets.
4. Measure simple sensitivities: calculate gaps, basis exposures and duration.
5. Run valuation models: produce EaR, EVE, convexity and scenario results.
6. Stress assumptions: vary deposit betas, decay rates, prepayment speeds, spreads and yield curves.
7. Compare with limits: escalate breaches to the asset–liability committee (ALCO).
8. Select actions: change pricing, funding, product structure, duration or hedges.
9. Monitor outcomes: back-test forecasts and document model performance.

A conceptual relationship is:

Figure: Integrated cycle for measuring and managing IRRBB.

10. Hedging and Managerial Decisions

Banks may manage IRRBB through product pricing, deposit strategy, funding tenor, investment allocation, securitisation, swaps, caps, floors, swaptions and balance-sheet growth choices. A pay-fixed, receive-floating interest-rate swap generally benefits from rising rates when it offsets a fixed-rate asset exposure; the opposite position may hedge floating-rate assets or fixed-rate funding. The hedge direction must be established from cash-flow and valuation sensitivities, not from instrument labels alone.

Hedge effectiveness depends on index, tenor, reset dates, notional amortisation, collateral terms and behavioural assumptions. Basis mismatch can leave residual risk. Derivatives also introduce counterparty, liquidity, collateral and legal risks.

Pricing decisions should incorporate a transfer price for interest-rate risk. Funds-transfer pricing (FTP) assigns funding and liquidity costs to products, helping business units recognise the value and risk of maturity transformation. Without effective FTP, loan pricing may appear profitable while transferring unpriced duration risk to treasury.

11. Governance, Regulation and Ethics

The board is responsible for risk appetite and oversight; ALCO sets policy and limits; treasury executes approved strategies; risk management independently measures and challenges exposures; internal audit evaluates controls. A sound framework includes documented assumptions, independent model validation, limit escalation, data lineage, stress testing and management reporting.

Regulatory expectations generally require banks to identify, measure, monitor and control IRRBB and to assess both earnings and economic-value effects. Specific supervisory thresholds and shock scenarios vary by jurisdiction and should be incorporated into local policy rather than assumed to be universal.

Ethically, management should avoid selecting assumptions merely to reduce reported risk or earnings volatility. Deposit stability, prepayment and discounting assumptions affect capital decisions and customer pricing. Material uncertainty should be disclosed, and model outputs should not be presented as precise forecasts when they are scenario-dependent estimates.

12. Technology and Contemporary Developments

Modern risk engines combine contract-level data, market curves, behavioural models and scenario generation. Cloud computing and distributed processing permit daily or intraday recalculation, while machine learning can assist segmentation and anomaly detection. However, AI models may be unstable under regime change, difficult to explain and vulnerable to data leakage. They should therefore supplement—not replace—economic reasoning, stress testing, validation and human accountability.

Contemporary challenges include rapid digital deposit migration, competition from money-market funds, volatile inflation expectations, changing central-bank transmission, climate-related transition effects on rates and increased demand for real-time liquidity. These developments make static historical assumptions less reliable and strengthen the case for adaptive but controlled model governance.

Illustrative Case: Meridian Bank’s Deposit and Mortgage Exposure

Background

Meridian Bank has 800 million in fixed-rate residential mortgages with effective duration 3.8 years. It funds them with 500 million of retail deposits and 200 million of three-month wholesale funding. Retail deposits have an estimated behavioural duration of 1.0 year; wholesale funding has duration 0.25 year. Equity and other funding account for the remainder.

Problem

Management believes the bank is protected because many deposits are low-cost and stable. However, a rapid rate increase could raise deposit rates and wholesale funding costs while mortgage income remains fixed. A fall in rates could increase mortgage prepayments, shortening asset duration and reducing expected income.

Analysis

Under a 1 percentage-point parallel increase, the approximate asset value change is:

−3.8 × 800 × 0.01 = −30.4 million

The deposit value change is approximately:

−1.0 × 500 × 0.01 = −5.0 million

The wholesale funding value change is approximately:

−0.25 × 200 × 0.01 = −0.5 million

Because liabilities are obligations, the EVE effect is approximated by the asset change less the liability change:

∆EVE ≈ −30.4 − (−5.0 − 0.5) = −24.9 million

This is a simplified estimate excluding equity duration, convexity, taxes, credit effects, deposit beta and hedges. Separately, the bank’s short-term NII may initially improve or deteriorate depending on the actual repricing speed of deposits and wholesale funding.

Approach and solution

ALCO segments deposits, estimates rate betas under up and down regimes, introduces a conservative behavioural-life cap, and runs mortgage prepayment scenarios. It adds a receive-floating/pay-fixed swap sized to the residual exposure, while retaining limits for basis and hedge ineffectiveness. Product pricing is revised using FTP so that new fixed-rate mortgages earn compensation for their duration and prepayment risk.

Outcome and learning points

The bank reduces EVE sensitivity but does not eliminate risk. The case demonstrates that contractual maturity is insufficient, EVE and NII can differ, and behavioural assumptions must be stress-tested. It also illustrates why hedging should be linked to risk factors—duration, index, tenor and optionality—rather than to broad asset categories.

Challenges and Limitations

IRRBB measurement is limited by uncertain customer behaviour, incomplete data, changing product design, non-linear options, model error and scenario ambiguity. Duration may fail for large shocks; gap analysis may ignore basis; EaR may understate long-term value loss; EVE may be dominated by assumptions about deposits and prepayments. Aggregation across currencies and legal entities can conceal local vulnerabilities.

Best practice is therefore not to seek one “correct” number. Instead, banks should maintain a measurement suite, explain drivers, compare contractual and behavioural views, perform reverse stress tests, and show the effect of alternative assumptions.

Chapter Summary

IRRBB arises from mismatches in repricing, reference rates, yield-curve exposure and customer options. Repricing gaps provide a simple earnings sensitivity, while basis gaps isolate differing index movements. Duration estimates first-order economic-value sensitivity; convexity improves the approximation for larger movements, but option-affected cash flows require revaluation. EaR focuses on future NII, whereas EVE measures the present-value effect on economic equity. Both are necessary.

Non-maturity deposits and prepayable loans require behavioural modelling, including deposit beta, decay, repricing lag and CPR/SMM assumptions. Effective management integrates contractual data, behavioural scenarios, stress testing, FTP, hedging and ALCO governance. Because assumptions can dominate results, independent validation, conservative limits, transparent reporting and ethical model use are essential.

Key Terms

Interest rate risk in the banking book: Risk of adverse effects from rate changes on banking-book earnings or value.

Repricing risk: Risk from unequal timing of asset and liability rate resets.

Yield-curve risk: Risk from non-parallel movements in rates across maturities.

Basis risk: Risk that linked reference rates move differently.

Option risk: Risk arising from contractual or behavioural exercise choices.

Rate-sensitive asset: Asset whose income resets within a specified period.

Repricing gap: Rate-sensitive assets minus rate-sensitive liabilities in a bucket.

Cumulative gap: Sum of repricing gaps through a selected bucket.

Macaulay duration: Present-value-weighted average timing of cash flows.

Modified duration: Approximate percentage price sensitivity to yield.

Convexity: Curvature of the price–yield relationship.

Earnings-at-risk: Estimated adverse change in NII under specified scenarios.

Economic value of equity: Present value of assets less liabilities and relevant positions.

Deposit beta: Sensitivity of administered deposit rates to market-rate changes.

Deposit decay: Expected reduction or runoff of deposit balances.

Prepayment: Early repayment of a loan before contractual maturity.

CPR: Annualised conditional prepayment rate.

ALCO: Committee responsible for balance-sheet and asset–liability risk oversight.

Funds-transfer pricing: Internal pricing system assigning funding and risk costs to products.

Model risk: Risk of adverse decisions caused by model defects, assumptions or misuse.

Review Questions

Short Answer Questions

1. What is the difference between repricing risk and basis risk?
2. Why should a bank use both NII and EVE measures?
3. State the simplified repricing-gap formula and explain its sign.
4. What does deposit beta measure?
5. Why can mortgage prepayments create negative convexity?

Long Answer Questions

1. Explain the construction, interpretation and limitations of a repricing-gap report.
2. Derive the duration-based approximation for the change in economic equity and discuss its assumptions.
3. Compare EaR and EVE as tools for ALCO decision-making.
4. Describe a governance framework for behavioural deposit and prepayment models.
5. Explain how basis, yield-curve and option risks can interact in a bank’s balance sheet.

Analytical / Application Questions

1. A bank has 600 million of assets with duration 3.5 years and 520 million of liabilities with duration 0.8 years. Estimate the EVE change from a 75-basis-point parallel rate increase, ignoring convexity and other effects.
2. A portfolio has RSA of 250 million and RSL of 310 million repricing over six months. Estimate the NII effect of a 1.5 percentage-point rate increase over that six-month period, and state the assumptions involved.
3. Design a stress-testing plan for a bank with fixed-rate mortgages, non-maturity deposits and wholesale funding. Identify at least four scenarios and explain the behavioural assumptions requiring validation.

Multiple Choice Questions with Answers

Question 1

A positive repricing gap in a time bucket means that:

A. Rate-sensitive liabilities exceed rate-sensitive assets

B. Rate-sensitive assets exceed rate-sensitive liabilities

C. Assets and liabilities have identical durations

D. The bank has no basis risk

Correct Answer: B. Rate-sensitive assets exceed rate-sensitive liabilities

Question 2

Under the simple gap approximation, a negative gap combined with a rate increase generally causes:

A. An increase in near-term NII

B. No change in NII

C. A decrease in near-term NII

D. An increase in EVE only

Correct Answer: C. A decrease in near-term NII

Question 3

Modified duration primarily measures:

A. Credit default probability

B. Approximate percentage price sensitivity to yield changes

C. Deposit runoff volume

D. The difference between two reference rates

Correct Answer: B. Approximate percentage price sensitivity to yield changes

Question 4

Which exposure is most directly associated with basis risk?

A. A loan linked to prime funded by a different interbank index

B. A fixed-rate bond held to maturity

C. A deposit with no contractual maturity

D. A foreign-currency cash balance

Correct Answer: A. A loan linked to prime funded by a different interbank index

Question 5

EVE is best described as:

A. The annual accounting profit before tax

B. The present value of assets less liabilities and relevant positions

C. The maximum daily deposit withdrawal

D. The contractual maturity gap

Correct Answer: B. The present value of assets less liabilities and relevant positions

Question 6

If market rates rise by 1% and a deposit beta is 0.40, the administered deposit rate changes approximately by:

A. 0.04%

B. 0.40%

C. 1.40%

D. 2.50%

Correct Answer: B. 0.40%

Question 7

For a constant monthly SMM, the relationship between CPR and SMM is:

A. CPR = 1 − (1 − SMM)¹²

B. CPR = SMM ÷ 12

C. CPR = 12 − SMM

D. CPR = SMM²

Correct Answer: A. CPR = 1 − (1 − SMM)¹²

Question 8

Why can prepayable mortgages exhibit negative convexity?

A. Prepayments tend to accelerate when rates fall, changing duration adversely

B. Their cash flows never change

C. Their liabilities reprice faster than assets by definition

D. They have no interest-rate sensitivity

Correct Answer: A. Prepayments tend to accelerate when rates fall, changing duration adversely

Question 9

Which measure is most directly focused on a specified future NII horizon?

A. EaR

B. Macaulay duration

C. Convexity

D. Economic value of equity

Correct Answer: A. EaR

Question 10

The primary purpose of independent model validation is to:

A. Guarantee that rates will not change

B. Replace ALCO decisions

C. Challenge assumptions, implementation and performance

D. Eliminate all hedging costs

Correct Answer: C. Challenge assumptions, implementation and performance